This story is a bit difficult to understand, so hang on tight: Read the details here, from The SEM Post.
So, Google's mobile-first index is apparently out in the wild. It's a small experiment right now and Google promises it will get bigger. Webmasters often maintain multiple versions of their pages. Some have desktop versions, some are responsive, some are desktop and mobile, and a few have AMP pages up already.
This has people wondering: what does the mobile index mean for me, given my specific site set-up?
If you have only a desktop version and AMP versions of your page: Google will use the desktop version for indexing. This is even after the mobile-first switch goes global.
If you have only AMP pages - no desktop site, no mobile site - then Google will use the AMP page for indexing.
I imagine that this only applies to a very thin demographic of webmasters, but worth mentioning.